Physics & astronomy · 1905

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen

Albert Einstein

Annalen der Physik · 4th series · vol. 17 · 1905

Einstein derives the random motion of particles suspended in a liquid and relates their mean displacement to diffusion.

Poster of “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen”: the text in four columns
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A2
License
Public domain
Retrieved
27 September 2026
Language
German
Rights holder
Albert Einstein, 1905

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Edition

Scan of Annalen der Physik, 4th series, vol. 17 (Leipzig: Johann Ambrosius Barth, 1905), no. 8, pp. 549-560, on the Internet Archive (sim_annalen-der-physik_1905_17_3, leaves 172 to 183). No proofread transcription was found (German Wikisource lists the paper with a scan link only): the text was built from the OCR of that scan and checked word by word against the page images, and every formula set from reading them, with a second scan of the same volume (annalenderphysi108unkngoog, digitized by Google) and its OCR as a cross-check; p. 554, where the OCR of the first scan lost most lines, was built from the OCR of the second. The title and “von A. Einstein.” are in the header; the byline restates in English the closing lines “Bern, Mai 1905.” and “(Eingegangen 11. Mai 1905.)”, which are also kept at the end of the text. The article number “5.” before the title, the running heads, page numbers and the signature lines of pp. 557 and 559 are left out, and hyphens at line ends are rejoined. The footnotes, numbered 1) on each page of the print, are numbered 1 to 3 and follow the text. Names set letter-spaced in the print are letter-spaced, words in italics are in italics, and the volume numbers of the references are in bold as printed; the two numbered processes of § 3 are set as paragraphs. Spelling, punctuation and misprints are kept, among them “eingelöstes Molekül” (p. 550), dz’_2 for dz’_1 in the first triple of primed differentials (p. 552, checked on both scans), the second equation numbered (1) (p. 558), f(x + Delta) without t in the integral of p. 557, phi(x) = phi(-x) (p. 557) and 3 pi k P under the root in the formula for lambda_x (p. 559). The number of particles per unit volume, printed as an italic Greek nu that looks like a Latin v, is set as nu; the sign between x and 0 on p. 558 is set as a greater-than over a less-than sign. The equations are set with KaTeX.

Rights

Albert Einstein died on 18 April 1955: his works are in the public domain in France since 1 January 2026 (70 years counted from 1 January 1956). The paper was published in 1905, before 1 January 1931, so it is in the public domain in the United States.

The Internet Archive scans used (sim_annalen-der-physik_1905_17_3, and annalenderphysi108unkngoog, marked “NOT_IN_COPYRIGHT”) are of the 1905 print; no image of them is reproduced.

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